Exercitiul 1
[tex] \frac{(n-4)!}{(n-2)!}= \frac{(n-2)!(n-3)(n-4)}{(n-2)!} = n^2-4n-3n+12 = n^2-7n+12 [/tex]
Exercitiul 2
[tex]C_{7}^{5}= \frac{7!}{5!2!} = \frac{5!*6*7}{5!*2!}= \frac{42}{2}=12 [/tex]
[tex]P7=7!=1*2*3*4*5*6*7=5040[/tex]
[tex]A_{7}^{5}= \frac{7!}{(7-5)!} = \frac{7!}{2!}= \frac{2!*3*4*5*6*7}{2!} = 2520[/tex]
Exercitiul 4
[tex] \frac{A_{15}^{5}+A_{15}^{6}}{A_{15}^{4}}= \frac{ \frac{15!}{10!} + \frac{15!}{9!} }{ \frac{15!}{11!} }=
[/tex]
[tex] \frac{ \frac{10!*11*12*13*14*15}{10!} +
\frac{9!*10*11*12*13*14*15}{9!} }{ \frac{11!*12*13*14*15}{11!} } =
\frac{360360+3603600}{32760}= 121[/tex]
